Non-Hermitian topological phase transition of the bosonic Kitaev chain

The bosonic Kitaev chain, just like its fermionic counterpart, has a topological phase with extraordinary properties. In general, all eigenmodes are exponential in position such that the x quadratures of the field are localized on one edge of the chain and decoupled from the p quadratures, which are localized on the other edge. In the topological phase, the modes conspire to lead to remarkable amplification of coherent light that depends on its phase and direction. In this work, we study this topological amplification for the bosonic Kitaev chain subject to different configurations of on-site dissipation. Specifically, we look at configurations that break the lattice's translation invariance but constitute unit cells of L sites. On the one hand, when the unit cell’s size is even, we find that the bosonic Kitaev chain exhibits topological amplification for arbitrarily large dissipation on odd sites---by far exceeding conventional expectations. On the other hand, even when subject to mild dissipation, the bosonic Kitaev chain undergoes a topological phase transition when the size of its unit cell is odd. Our work thus provides insights into topological amplification of multiband systems and sets explicit limits on the bosonic Kitaev chain's ability to act as a multimode quantum sensor.